MICROFICHE APPENDIX I contains one page of microfiche with 51 frames and is a printout of source code for executing steps of an illustrated embodiment of the invention".
MR imaging is most commonly performed with 2D FT or 3D FT techniques, which require only a modest amount of prior knowledge about the object: 1) the object is assumed to be completely contained within a finite field of view (FOV); 2) the image is assumed to be band-limited in frequency space; i.e. its significant power spectrum does not extend beyond some maximum spatial frequency. If these two assumptions are valid, the usual sampling theorem (due to Whittaker, Kotel'nikov, and Shannon, or WKS, (1-4)) states that the image can be reconstructed by an inverse FT of a finite number of discrete samples of the image's k-space representation. The spacing between the sampled k-space points is determined by the first assumption (the dimensions of the FOV), and the limits of the k-space sampling pattern are determined by the second assumption (the maximum spatial frequencies in the image). This method is widely used because: 1) it is based on relatively weak assumptions about the image, 2) it is relatively easy to acquire the Fourier-encoded signals stipulated by the WKS theorem, and 3) image reconstruction can be performed efficiently with a fast FT (FFT).
In contrast-enhanced carotid artery imaging, interventional imaging, functional imaging, cardiac imaging, and a number of other applications, the utility of MRI is limited by the speed with which the k-space data can be measured. Two general strategies have been used to shorten image acquisition time. 1) Gradient pulses with shorter rise times and/or larger amplitudes have been used in order to shorten the time required to gather a complete WKS data set. Unfortunately, gradient ramp rates and strengths are now approaching values at which neuromuscular stimulation can compromise patient safety and comfort. 2) More stringent assumptions can be made about the image in order to reduce the number of signals necessary to reconstruct it. Some of these "constrained imaging" methods simply apply WKS sampling with stronger assumptions in order to increase the spacing between k-space points (reducing the FOV) or to reduce the k-space sampling limits (reducing image resolution). More novel approaches have utilized prior knowledge to express the image as a superposition of a small number of non-Fourier basis functions. The image's projections onto these basis functions are computed from a reduced set of Fourier-encoded signals, or they are measured directly by performing non-Fourier encoding.
In this invention, we take a different approach. We generalize the WKS sampling theorem so that it can be applied to images which are supported on multiple regions within the FOV. By using this "multiple region MR" (mrMR) sampling theorem, such images can be reconstructed from a fraction of the k-space samples required by the WKS theorem. Image reconstruction is performed with FFTs and without any noise amplification, just as in conventional FT MRI. In addition, we show how the method can be applied to a broader class of images having only their high contrast edges confined to known regions of the FOV. If this kind of prior knowledge is available, k-space can be sampled sparsely, and scan time can be reduced. The next section describes the theoretical framework of the mrMR approach. Then, the method is illustrated with simulated data and with experimental data from a phantom. Finally, we describe how the method was used to reduce the time of first-pass Gd-enhanced 3D carotid MRA so that it could be performed without bolus timing.